PBwiki does not have support for an arbitrarily large set of subgroups of users to have different access to a wiki; i.e., ACLs that vary per-page. (Incidentally, such setups are a nightmare to administer.)
It does, however, allow premium wiki admins to invite individuals to participate at specific access “levels” such as “Reader”, “Contributor”, “Moderator”, or “Administrator”. Given that we allow control of user-level access to the wiki on a per-level basis, most people would call this “supporting access control lists”.
See also